DOMINANT PREPARATION -- Now where did I put that darned whip again? (III)

DOMINANT PREPARATION -- Now where did I put that darned whip again? (III) - 08/09/0408:36 PM

We've already established the dominant/tonic relationship as one of the most fundamental harmonic structures of Western music. These two functions come in quite handy in establishing and solidifying the harmony of a musical piece. But, as we've seen from discussions about triads, there are potentially seven diatonic triads available in any key's vocabulary. If the tonic and dominant were the only harmonies used, things would get pretty dull really quickly (despite the fact that many simple songs do just that).

So, let's dismiss both the tonic and dominant triads for now, since we already know what they do, and toss out the leading tone triad as well since it functions the same as a dominant triad (yes, we'll discuss this later). That leaves us with four remaining triads: the supertonic, mediant, subdominant and submediant. Just what the heck is the normal use for these triads? Well, wouldn't you like to know!

Considering the title of this-here lesson, I'm guessing that you're mumbling under your breath, "dominant preparation, whatever that is." Of course, you mutterers, that's exactly right. We still haven't defined just what dominant preparation is, though, so let's get right to that. If one were to analyze the harmony of a huge number of short harmonic phrases with cadential endings, a pattern looking something like this would become evident:

I _ _ _ _ _ _ _ _ _ V I

In this particular game of hangman, though, there is no set number of blanks to fill in, nor, necessarily, have all of the I's and V's been placed into the puzzle. This big blank spot is what we call dominant preparation. The harmony progresses in a hierarchical fashion up to the final dominant, preparing the way, as it were. It's all just a big setup, building a framework of support for that last big dominant at its peak. (Which, naturally, is followed by an even bigger collapse to the tonic at the end!)

I know we keep harping on this, but that dominant/tonic relationship is really very strong. Part of its strength lies in the relationship of a fifth between the tonic and dominant. Motion down by a fifth is, of course, the hallmark of the circle of fifths, and this motion is important enough that it plays out fairly consistently in dominant preparation. Only in the case of dominant preparation, we need to work {gasp} backwards! You see, if the drop of a fifth from dominant to tonic is strong, it follows that other, similar drops of a fifth are strong, too.

(NOTE: all following references to triads by Roman numeral identification are intentionally left all UPPER case, but should not be construed as Major triads. All triads referred to herein are diatonic.)

So, let's work our way backwards from the dominant, moving up a fifth, so that we can drop down to V. A fifth up from V would land us on the supertonic, scale degree II. Moving up a fifth from the supertonic by a fifth puts us at the submediant, scale degree VI. Going up a fifth from the submediant takes us to the mediant, III. Up a fifth from the mediant takes us to the leading tone, VII, which we've already decided to sort of ignore. Up a fifth from the leading tone takes us out of the diatonic scale (bummer), so that's about as far as we can go. So, at this juncture, our backwards progression (starting at the tonic) goes I - V - II - VI - III - (VII).

OK, that covers six of the seven triads. Where does IV fit in? Curiously, if doing a strict circle of fifths, it would have to be at the beginning of the list (down a fifth from I). Putting it all together (still backwards, mind you), we end up with:

IV - I - V - II - VI - III - (VII) [/b]

Look closely at where V stands in this sequence, and we can see the relative strength of the motion between any triad and the dominant. The further from V a triad is on the line, the weaker the motion. Thus, we could say that motion from II to V is very strong, whereas motion from III to V is much weaker.

Now, let's look at a few observations that were made about the order in which dominant preparation harmonic progressions move. Just remember, these aren't "rules" for writing music, these are principles based on the observation of what had already been written. Were the composers who wrote this music cognizant of these principles? Perhaps, but the principles were not codified until afterwards. All that notwithstanding, there was great emphasis on the circle of fifths in late Renaissance and early Baroque music, and it is likely that study of the circle of fifths is the basis of most of these principles.

First, we'll note that when one chord follows another, the progression is from weaker to stronger motion towards the dominant. Progression from strong to weak would be considered retrograde progression, something that was usually avoided. Then let's temper that by saying that any triad can go to either I or V, with the notion that any move to I or V within a progression acts as a reset button; any previous pattern of motion is nullified by inserting either.

For example, in the following, look at the second instance of I, on the third beat of the first measure.

Here, it separates IV from iii. Normally, a move from IV to iii would be considered retrograde (ick!), but the insertion of I between them resets the progression, so that this is not retrograde motion. Starting with the fourth beat in the first measure, we resume with iii, a weak dominant preparation, followed by vi which is stronger. vi is then followed by ii, a even stronger dominant preparation. Then what happens?

Oh, no! The dreaded cadential I6/4 chord! Don't worry, the cadential I6/4 and the following V7 chord are all the greater dominant function. (Another part of another lesson!) So, with all that dominant preparation out of the way, we were able to set up the dominant and have a nice, grand ending cadence.

Let's also look at our circle of fifths list again, only this time, we'll put it in forward order (we'll leave VII out of the picture):

III - VI - II - V - I - IV[/b]

Following this order from III through I we can see what would be considered a normal harmonic progression of dominant preparation and cadence. Yet, that poor IV sitting there at the end does present a bit of a problem when viewing it strictly in terms of circle of fifths progression. But theorists noted that it does work just fine as a dominant preparation chord if it is considered as equivalent to VI (with which it shares 2 notes), and in terms of relative distance from the dominant, they are the same distance.

So, really, what good is all this talk about dominant preparation? Does it serve any purpose to us, as aspiring musicians? The answer is an unqualified "yes." Its real functionality comes into play when harmonizing a melody. If you can remember the relative strength of each of the dominant preparation chords, you can supply an appropriate underpinning of harmony in a progression that is functionally equivalent to those done by countless other musicians faced with the same task.

You're probably still wondering... "Is this the only way?" Of course, there have been deviations from the most common progressions. Composers eagerly sought ways to spice things up a bit, and, at times, even a "retrograde" progression suited the needs at hand. But, these are exceptions that require quite a bit of deliberate flouting of the norms of common practice, and are best left to those who can apply them judiciously in special circumstances.

The exercises I have supplied here are rather simple, and your goal here is to determine whether the sequences of dominant preparation in these examples do or do not follow the patterns we have discussed in this lesson. For each example, write out the harmonic progression using Roman numeral notation, then choose whether the progression is "normal" or "retrograde".

#1.

#2.

#3.

#4.

Answers on Friday!

This week's garden tip: Many woodland plants have been appropriated for use in gardens as ornamentals. Plants native to temperate forests often thrive in soil pH conditions that are made acidic by the leaf litter that carpets the forest floor. If your garden contains such plants, but you notice that they seem a bit yellowish in leaf color, spindly or stunted, you may need to decrease your garden's soil pH so that these plants can better absorb nutrients from the soil. This can be accomplished in a number of ways, but for a quick turnaround, consider applying granulated iron sulfate to those areas where your acid-loving plants are located. In addition to lowering the soil's pH, iron sulfate will also supply iron for your plants, a trace nutrient required by almost all plants.

Next week's topic: INTERVALS -- What you don't know CAN hurt you! (I)[/b]

Matt, thank you, thank you, THANK YOU! For taking the time to post these wonderful instructions and exercises. I love the way they're written and even though I don't understand most of them yet, I know that once I do some catch-up in theory, I'll be there with you.

I'd almost ask Frank for a separate Matt G. forum, but it may be better to leave them here in the AB forum for better exposure. I'll content myself with copying them into Word so I can keep them organized.

Originally posted by enescu:Are all these facts and principles coming into music from inside us?Was there music first, then principles were recognised and understood? [/b]

Precisely. It seems that we innately understand the mathematical aspects and patterns in music, and music theory came along well after the fact to help us analyze just what it is that we already understand! The music came first, then some wise guys figured out what made it tick.

Thanks for the augmented examples, Matt. I want ii thank you IV your efforts here II. (or perhaps one needs the extra "I" in the adverbial form of II, making it III? ... Oh well its probably just A- point. ) Whenever I feel a bit diminished these threads seem to make me feel better ... a kind of tonic, or perhaps even a super-tonic.

I think Kk may be just trying to work out the kinks in her understanding of the concept "retrograde". Or perhaps she misread it as "reprobate" and made the tomK-onnection that way. (Lets hope it doesn't raise the caffeine level in here too much though )

(with all those I-resets, it didn't hardly have a chance to get retrograded very much, did it?)

Oh, by the way, speaking of southern Illinois, there's a piano teacher at the university in Carbondale named Donald Beatie who is an acquaintance of mine and is a very energetic and vibrant teacher ... very popular in particular to music lovers majoring in non-music subjects.( His wife teaches music there too and is very popular with those who just love beauty in general. ) Anyway, your mention of meeting other folk hailing from that area reminded me of him, and I thought I just might mention his name on the slight chance that you might know of him as well. He's the guy that rounded up 14 other piano professors, put them on 7 or 8 grands and pounded out several of the Beethoven symphonies. Pretty impressive.

Well, katie, we figured it was for your own good, as some of the more inventive recipes for "miles & miles of green greasy gopher guts" can get pretty gruesome.

And me without a (tuning) fork.

Does anyone know the German letters used for the scale tones? I know they used the letter "H" or Schumann couldn't have written his "Variations on BACH ". What is this leading up to? Don't ask, but think about what the title of this lesson might be if H WAS the dominant.

Music flounders without a regular pulse and it is not enough to merely harmonize a melody with a random selection of bass notes as given in Matt's 5 examples.

It is important to create a composition balance between the roles of the two hands- ONLY ONE (melody or directional motif) can be the "boss" - the other must chime a simple FORWARD MOVING PULSE.

In Nocturne Op. 9 , no.2 Chopin uses a regular forward pattern of notes (bass followed by two chords) to drive his music forward. Beethoven settles for the drumming effect of 8 identical arpegiated "triplets" against which to sound his LH octave chords in the opening measures of his "Moonlight" Sonata. Bach's WTC Prelude I uses the same formula.

Sadly Matt's examples display the typical wooden musical effect of most hymns in the hands of amateur musicians who go overboard in digging up rules from dusty books on harmony and counterpoint - and lose the plot.

In picking up the treble melody lines of "Hark The Herald Angels Sin" (forgive the pun), "God Save The Queen", "Auld Land Syne" and "Good King Wenceslas", the bass ought not to adopt a random harmonized "wandering" but follow a clear even pulse.

I have just enjoyed playing through a few top pops of our day to remind of the above principle -in all cases THE BASS IS KEPT TO A SIMPLE OUTLINE SO AS NOT TO COMPETE WITH THE POTENT MESSAGE DELIVERED IN THE TREBLE - a sure sign of a "poet of the piano".

Might I recommend a study of the haunting hits:

"Maria" by Leonard Bernstein"By the Time I Get to Phoenix""Out of My Dreams" by Richard Rodgers"I Got Plenty O' Nuttin'" by George Gershwin

When young hopefuls gush "even though I don't understand most of them yet, ... " we can start to worry - a case of the blind leading the blind.

Originally posted by btb:When young hopefuls gush "even though I don't understand most of them yet, ... " we can start to worry - a case of the blind leading the blind.

Thanks for the rant. [/b]

First off, pay attention. This is not a forum for "young hopefuls," this is a forum for new and returning adult[/b] students. Second, these lessons are not an attempt to teach anyone accompaniment styles. This is music theory, not a piano playing practicum. Third, despite your slurs, music theory is not a bunch of "old dusty rule books." If that's your impression, you are sorely mistaken. Someone, it seems, had a bad experience with a bad teacher. Fourth, read up on the intended scope and format of these lessons here.

Now, if you will excuse us, I (not blind, although I am nearsighted and do have some pretty bad astigmatism, along with the usual presbyopia for someone my age) was preparing to give out the answers to this week's wooden, amateurish exercises to the poor misguided sheep who are actually paying attention.

Matt; great job with the music theory lessons. I think I speak for most of us who tune in every week when I say we really appreciate how much time and effort you've been putting into these lessons. I've been copying and pasting your lessons into a Word document for later review and reference and I believe I'm up to 20 pages of lessons. That's a tremendous effort for someone who is doing this simply because we asked nicely. So, a big "thanks" again for helping to teach us adult students.Jon

Ach I hit the add instead of preview before I was done. Any way this is what I have so far and I'm kinda stumped with the normal/retro thing with all the "resets" in there. Let me know if I'm at least right on the chords Cathy

Kathy I agree with you (except for a couple of to "to 7 or not to 7" ) everywhere except for :

Example 3, (auld lang whatever) Measure 2, Beat 2&, which I see as a d7, which would be vi7 rather than vii7. I figure good chance it was a typo.

As far as Normal and Retrogressive. 1 Hark: normal all the way

2 God Save the Queen: M2 Beats 1,2,3 goes V vi V I so that little part is retrograde, I think.same song, [ M3 B4] , [ M4 B1,2,3 ] goes ii7 iii ii I so that part is retrograde too, I think, (just the ii7 iii part, I guess to be more precise.) (just trying to avoid more Pretorian epithets)

Okay I see that one; the typo excuse sounds as good as any. I think I need some clarification on the normal vs retrograde. If everything is going along normal but all of a sudden we get a chord out of sequence before a "reset" does that make it retrograde?

For NORMAL progression, you work left to right, never "backtracking" to the left.

i.e. if you play a VI chord you would continue to right, say VI, II, I ... or VI, V, I ... but NOT VI, III[/b]...(which is to the left of VI, or "farther away" from the root)..., VI, II, I. Well, you CAN jump to the left, but that IS the definition of retrograde. (I think.)

I may be exaggerating or misjudging a bit, but retrograde progressions seem to have a kind of "minor" or "unsettled" sounding quality about them. Not out of place, but a bit different and noticeable.

There may be "cautions of (size) scale" involved here too, as these passages are pretty short, and longer ones with several phrases might show better retrograde examples.

I'm not sure how retrogrades work with key or tonal center changes, but I'm sure they are linked fairly closely. The last two chords in AuldLangSang, for instance, while being I, IV in F are V, I in Bb. I really hate this song, or I'd go look it up to see if the next phrase is centered around Bb instead of F. (sorry, I just must have heard too much of Guy Limburger's 34" vibrato on this song ) :rolleyes:

I guess it takes a while to carve those little wooden answers to those not so little wooden exercises. (Tapping my big wooden shod toe. :p )

I guess next week's lesson will now be late. Now that Matt understands that his little example ditties are expected to catch on like wildfire and make the Top Forty by the end of the week. We have a right to expect them to have made Safeway's Muzak in not more than a fortnight. If little old church ladies aren't humming them while window shopping we just aren't getting what we paid for. :p

I have a question concerning chord terminology that might fit in here. I'm going to hammer it in anyway, so objections are pointless.

I know Matt called in sick a couple of days ago, so I don't expect an instant answer, unless its "Why don't you just GO TO BED already?"

Is there a term for 2-tone chords, or chords that are missing one of the main triad notes (1,3 or 5)I've heard "power chord" used when just the root and the 5th is played, and I'm not sure how "power" became the chosen word, but that's not the aspect of the question I'm interested in right now.

For the situation I'm thinking of, the word "open" or "ambiguous" or "transfer" might work better.

I've got a piece (Sheep may safely graze, Bach) that's been in Bb Major for 20 measures (except for a brief 4 measure foray into F quite a ways back. The piece is heading for Cminor and gets there by going from Bb Major to Gminor for 4 measures and then hitting Cminor for several more measures (8 or 10 or 12)after that.

Measure 21 FIRST chord contains 3 Bb's and 1 D, while the next chord adds a G so it has Bb, D, D, G

So the second chord is a Gminor triad, while the first chord could be Bb Major triad if an F was added, or a Gminor triad if a G had been added.

My point is that it is a kind of swing chord ... it is almost the Bb that the last 2 F chords in Measure 20 would normally fall too and its almost the Gminor triad that the next 4 measures are rooted on.Seems like there might be a tidy little name for this thing... "modulating ambiguosichord " or something. (hopefully something other than THAT.)

A similar thing happens 2 measures later as the tonal center shifts from Gminor to Cminor.

The chords up to then are g?Bb? (the chord mentioned above) g,D7,g, |bar| Ahalfdim, D , g, and then 2 more ambiguous chords, dX and G7X

(beat 4) F G D A and (beat 4&) F G D GThe first would be some form of a Dminor chord, and the second some form of a G(Major or Minor)7th chord, but the Bb or B which would declare it as a major or minor is missing.

(the next chord is a Cminor triad which sets the tone for the next several measures)so the progression to the first Cminor chord, (as expressed in Cminor) would be ii . (V7 or v7), i

I see the point of leaving the determining note out of the chord ... it makes the transition a bit less abrupt ... but I'm just wondering if there is an accepted or common terminology for the technique or the chords used.

I can clean the cat hair off my flatbed and scan and post this part of the score it its not clear enough above. (Cats: can't live with em , can't live with[/b] em. )

I like it. I first heard it on David Duval's "Reflections from the Keyboard" radio program, where someone played "Blithe Bells", which is Percy Graingers arrangement of this piece.

Egon Petri's arrangement, mentioned on PW early this June and serendipitously and surreptitiously forwarded to me by the illustrious Ms. Tunes of Tweksbury Mass, who also went to the considerable trouble of sheathing each page in one of those clear plastic page protectors. ) was one of Victor Borge's piano teachers.

Bob (Sorry for the delay in aswering your post. I got busy and js now got bach to it. )

OK, sorry for the delay. I'm almost well now, so I managed to put the answer's to last week's lesson together. (I think THIS week's lesson will become NEXT week's.) Now, with the sharpened chisel , let's look at the answers. (Numbers in parentheses indicate inversion, | = bar line.)

This one is normal, with nothing out of the ordinary, unless you got surprised in the second full measure going from V7 to vi7. This is considered a deceptive resolution (remember deceptive cadences?), but not retrograde. How'd you like the half cadence on IV? That's pretty rare, but, as you can see, it still works.

An interesting harmonization, don't you think? Did it sound a bit off, though? Notice that m. 2 ends on V (half cadence), but the first chord in m. 3 is IV. This might be acceptable, depending on context, but here it just sounds weird. But m. 3 also has the IV going to iii (oops, that's retrograde, now isn't it), which makes for an even weirder sound.

Originally posted by RKVS1: Is there a term for 2-tone chords, or chords that are missing one of the main triad notes (1,3 or 5)I've heard "power chord" used when just the root and the 5th is played, and I'm not sure how "power" became the chosen word, but that's not the aspect of the question I'm interested in right now.

For the situation I'm thinking of, the word "open" or "ambiguous" or "transfer" might work better.[/b]

For want of a better term, I would call them "ambiguous" in most contexts. Generally, it is the third above the root of a triad that is the determining tone in whether the triad is major or minor. An open 5th with no intervening 3rd is ambiguous. It could be used in a number of places where one wanted to keep the harmony ambiguous, but for the most part that would have been considered a non-standard usage.

As for calling them "power chords," this is a terminology (and technique) originally used by guitar players, who wanted to make their part in an ensemble more prominent. By using only the root and fifth of the chord, they get more volume (and strangely enough, even on the piano, you'll get overtones that suggest a major chord).

Measure 21 FIRST chord contains 3 Bb's and 1 D, while the next chord adds a G so it has Bb, D, D, G

So the second chord is a Gminor triad, while the first chord could be Bb Major triad if an F was added, or a Gminor triad if a G had been added.[/b]

OK, don't get too worked up over this particular one. A fairly common voicing for a chord could just be the root and the third (recall what I just said about it being the determinant interval), often with the root tripled. In fact, this is such a common resolution for a dominant (well, looky there, that's what precedes it!) that it is given special consideration.

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Bob continues....My point is that it is a kind of swing chord ... it is almost the Bb that the last 2 F chords in Measure 20 would normally fall too and its almost the Gminor triad that the next 4 measures are rooted on.Seems like there might be a tidy little name for this thing... "modulating ambiguosichord " or something. (hopefully something other than THAT.)[/b]

Ah, yes, well, isn't g minor the relative minor to Bb Major? Actually, even if one were to ignore the triple-root idea presented just above, the resolution from the dominant to the submediant is very commonly referred to as a deceptive resolution (see what I wrote above about this), which also underscores the whole Major/relative minor relationship.

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Yes, even more Bob...A similar thing happens 2 measures later as the tonal center shifts from Gminor to Cminor.

The chords up to then are g?Bb? (the chord mentioned above) g,D7,g, |bar| Ahalfdim, D , g, and then 2 more ambiguous chords, dX and G7X

(beat 4) F G D A and (beat 4&) F G D GThe first would be some form of a Dminor chord, and the second some form of a G(Major or Minor)7th chord, but the Bb or B which would declare it as a major or minor is missing.

(the next chord is a Cminor triad which sets the tone for the next several measures)so the progression to the first Cminor chord, (as expressed in Cminor) would be ii . (V7 or v7), i[/b]

Here's a handy hint for deciphering weird chords: rearrange them so you can stack them in thirds (all lines or all spaces). When dealing with extended harmonies, it is common to leave many of the notes out of the stack. So your first chord (FGDA) stacks D F A (C) (Eb) G, an 11th chord. 11th chords are usually just suspensions, though. Check the harmony just prior: is there a G that appears to be held over?

The second (FDGD) stacks G (Bb) D F; a 7th chord. Wait, no third??? OK, let's see what follows: a c minor chord. Hmm, sounds like a secondary dominant (or if you're going to c minor, then the dominant in c minor). Why no third? Sometimes voice leading can lead you into a strange spelling for a chord. It happens.

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and finallyI see the point of leaving the determining note out of the chord ... it makes the transition a bit less abrupt ... but I'm just wondering if there is an accepted or common terminology for the technique or the chords used.[/b]

Actually no, this is not really any particular technique. A composer will make lots of decisions on voicing harmonies in deference to voice leading (making the inner voices smoother with mostly stepwise motion) or playability, especially for keyboard instruments. In this particular case, it was apparently felt acceptable that the third be omitted in favor of, most likely, one or the other of the above.

As an extra-added aid in understanding some of the concepts I've presented in this lesson, I'd like you to take a look at this cool little gadget that Frank B. is making available at his pianosupplies.com site: the Circle of Fifths Clock ! Even if you don't buy one, print a copy of the clock face; it's a much better visual than I can possibly render here by typing.

I bought one of those Circle-of-Fifths clocks for my oldest son when he first went off to college, but I screwed up the order and got the one with a digital readout by mistake. (You have to be really good at theory to read THAT puppy!

Thanks for the feedback on my questions, Matt. I'll have to look more closely at the score when I get home to check for that held-over G.